## ANOVA Multiple Choice Questions Quiz

1. Analysis of variance is a statistical method of comparing the of several populations.
A. Means
B. Variances
C. Standard Deviations
D. None Of The Above

2. The…..sum of squares measures the variability of the observed values around their respective treatment means.
A. Error
B. Total
C. Treatment
D. Interaction

3. Which of the following is an assumption of one-way ANOVA comparing samples from three or more experimental treatments?
A. The samples associated with each population are randomly selected and are independent from all other samples
B The response variable within each of the k populations have equal variances
C All the response variables within the k populations follow a normal distributions
D. All of the above

4. When the k population means are truly different from each other, it is likely that the average error deviation:
A. is relatively small compared to the average treatment deviations
B. is about equal to the average treatment deviation
C. is relatively large compared to the average treatment deviations
D. none of the above

Answer: is relatively small compared to the average treatment deviations

5. In a study, subjects are randomly assigned to one of three groups: control, experimental A, or experimental B. After treatment, the mean scores for the three groups are compared. The appropriate statistical test for comparing these means is:
A. The Analysis Of Variance
B. The Correlation Coefficient
C. Chi Square
D. The T-Test

6. When conducting an ANOVA, FDATA will always fall within what range?
A. between 0 and infinity
B. between 0 and 1
C. between negative infinity and infinity
D. between 1 and infinity

7. Assume that there is no overlap between the box and whisker plots for three drug treatments where each drug was administered to 35 individuals. The box plots for these data:
A. represent evidence against the null hypothesis of ANOVA
B. provide no evidence for, or against, the null hypothesis of ANOVA
C. represent evidence for the null hypothesis of ANOVA
D. none of the above

Answer: represent evidence against the null hypothesis of ANOVA

8. An investigator randomly assigns 30 college students into three equal size study groups (early- morning, afternoon, late-night) to determine if the period of the day at which people study has an effect on their retention. The students live in a controlled environment for one week, on the third day of the experimental treatment is administered (study of predetermined material). On the seventh day the investigator tests for retention. In computing his ANOVA table, he sees that his MS within groups is larger than his MS between groups. What does this result indicate?
A. An error in the calculations was made
B. There was more than the expected amount of variability between groups
C. There should have been additional controls in the experiment
D. There was more variability between subjects within the same group than there was between groups

Answer: There was more variability between subjects within the same group than there was between groups

9. In ANOVA with 4 groups and a total sample size of 44, the computed F statistic is 2.33 In this case, the p-value is:
A. greater than 0.05
B. exactly 0.05
C. cannot tell – it depends on what the SSE is
D. less than 0.05

10. What would happen if instead of using an ANOVA to compare 10 groups, you performed multiple t- tests?
A. Making multiple comparisons with a t-test increases the probability of making a Type I error
B. Sir Ronald Fischer would be turning over in his grave; he put all that work into developing ANOVA, and you use multiple t-tests
C. Nothing serious, except that making multiple comparisons with a t-test requires more computation than doing a single ANOVA
D. Nothing, there is no difference between using an ANOVA and using a t-test

Answer: Making multiple comparisons with a t-test increases the probability of making a Type I error

11. What is the function of a post-test in ANOVA?
A. Describe those groups that have reliable differences between group means
B. Set the critical value for the F test (or chi-square)
C. Determine if any statistically significant group differences have occurred
D. None of these

Answer: Describe those groups that have reliable differences between group means

12. Assuming that the null hypothesis being tested by ANOVA is false, the probability of obtaining a F- ratio that exceeds the value reported in the F table as the 95th percentile is:
A. equal to .05.
B. greater than .05.
C. less than .05.
D. None of these

13. Assuming no bias, the total variation in a response variable is due to error (unexplained variation) plus differences due to treatments (known variation). If known variation is large compared to unexplained variation, which of the following conclusions is the best?
A. There is evidence for a difference in response due to treatments
B. The treatments are not comparable
C. There is significant evidence for a difference in response due to treatments
D. There is no evidence for a difference in response due to treatments

Answer: There is evidence for a difference in response due to treatments

14. The……sum of squares measures the variability of the sample treatment means around the overall mean.
A. Error
B. Interaction
C. Total
D. Treatment

15. If the true means of the k populations are equal, then MSTR/MSE should be:
A. close to 1.00
B. close to -1.00
C. a negative value between 0 and – 1
D. more than 1.00

16. If the MSE of an ANOVA for six treatment groups is known, you can compute
A. the pooled standard deviation
B. the standard deviation of each treatment group
C. df1

17. To determine whether the test statistic of ANOVA is statistically significant, it can be compared to a critical value. What two pieces of information are needed to determine the critical value?
A. MSTR, MSE
B. mean, sample standard deviation
C. expected frequency, obtained frequency
D. sample size, number of groups

Answer: sample size, number of groups

18. The error deviations within the SSE statistic measure distances:
A. between groups
B. within groups
C. both (a) and (b)
D. None of the above

19 As variability due to chance decreases, the value of F will
A. Decrease
B. Stay The Same
C. Increase
D. Canâ€™t Tell From The Given Information

20. In one-way ANOVA, which of the following is used within the F-ratio as a measurement of the variance of individual observations?
A. SSE
B. MSE
C. MSTR
D. none of the above

21. If FDATA = 5, the result is statistically significant
A. Sometimes
B. Always
C. Never
D. None Of The Above

22. You obtained a significant test statistic when comparing three treatments in a one-way ANOVA. In words, how would you interpret the alternative hypothesis HA?
A. At least two treatments are different from each other in terms of their effect on the mean response
B. Exactly two of the three treatments have the same effect on the mean response
C. All three treatments have different effects on the mean response
D. None of the above

Answer: At least two treatments are different from each other in terms of their effect on the mean response

23. You carried out an ANOVA on a preliminary sample of data. You then collected additional data from the same groups; the difference being that the sample sizes for each group were increased by a factor of 10, and the within-group variability has decreased substantially. Which of the following statements is NOT correct.
A. The degrees of freedom associated with the treatment term has increased
B. The degrees of freedom associated with the error term has increased
C. FDATA has changed
D. SSE has decreased

Answer: The degrees of freedom associated with the treatment term has increased

24. ANOVA was used to test the outcomes of three drug treatments. Each drug was given to 20 individuals. The MSE for this analysis was 16. What is the standard deviation for all 60 individuals sampled for this study?
A. 4
B. 6.928
C. 48
D. none of the above